3D numerical simulations and microstructural modeling of anisotropic and tension–compression asymmetric ductile materials

Abstract

In the present work, we have analyzed the effect of anisotropy on void growth and stress–strain behavior for materials that exhibit remarkable tension–compression asymmetry (i.e., zirconium alloys). For that purpose, we have performed finite element simulations using a cubic 3D cell with a spherical void inside and subjected to periodic boundary conditions. Nonlinear kinematic constraints are also imposed as boundary conditions in order to maintain the values of macroscopic ratios constant during the whole loading history of the cell and account for a general (3D) stress state. The behavior of the matrix material is described by the CPB06 anisotropic criterion developed by Cazacu et al. (2006). The numerical results are compared to those considering 3D homogeneous (without void) cell with the same initial porosity as the voided one and governed by the anisotropic porous yield criterion developed by Stewart and Cazacu (2011). To investigate the influence of prescribed stress, strength differential parameter and strain hardening exponent on stress–strain behavior and void growth in the non-homogeneous (with void) and the homogeneous (without void) cells, we have used several stress ratios, three strength differential parameters and three strain hardening exponents. Finite element results obtained from different stress ratios show the strength differential parameter significantly affect void growth in both homogeneous and non-homogeneous cells. Moreover, comparison of two cells proves that both stress–strain behavior and porosity evolution are in good qualitative agreement for all three values of strength differential parameter. In contrast, as the value of strain hardening exponent increases, the agreement between results obtained from homogeneous and non-homogeneous cells is worse. An heuristic extension of the Stewart and Cazacu (2011)’s model is proposed in this work in an attempt to improve the accuracy of the model.